Finite Group Databasebeta

← Group #281156

Character table — Group #281156

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-11
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111-1-1-111-1-1111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1111-1-111-1-1-11
χ91111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ101111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-111-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-1-11111-1-11-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11-111-1-111-1-11-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-11-1-111-1-111-11
χ172222222222-2-22-2-220000-2-22222-2-2-2-2000022-2-2000000000000000000-220000000000
χ182222222222-2-22-2-220000-2-22222-2-2-2-20000-2-2220000000000000000002-20000000000
χ192222222222-2-22-2-220000-2-2-2-2-2-2222200002222000000000000000000-2-20000000000
χ202222222222-2-22-2-220000-2-2-2-2-2-222220000-2-2-2-2000000000000000000220000000000
χ2122222222-2-222-222-22222-2-20000000022-2-20000-2-222-2-2000000000000000000000000
χ2222222222-2-222-222-22222-2-200000000-2-2220000-2-2-2-222000000000000000000000000
χ2322222222-2-222-222-2-2-2-2-2-2-20000000022-2-2000022-2-222000000000000000000000000
χ2422222222-2-222-222-2-2-2-2-2-2-200000000-2-22200002222-2-2000000000000000000000000
χ2522-2-22-2-22002-202-2022-2-200i2i2−i2−i2i2i2−i2−i2002-2000000002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ2622-2-22-2-22002-202-2022-2-200i2i2−i2−i2i2i2−i2−i200-2200000000-22i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ2722-2-22-2-22002-202-2022-2-200−i2−i2i2i2−i2−i2i2i2002-2000000002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ2822-2-22-2-22002-202-2022-2-200−i2−i2i2i2−i2−i2i2i200-2200000000-22−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ2922-2-22-2-22002-202-20-2-22200i2i2−i2−i2i2i2−i2−i2002-200000000-22−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ3022-2-22-2-22002-202-20-2-22200i2i2−i2−i2i2i2−i2−i200-22000000002-2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ3122-2-22-2-22002-202-20-2-22200−i2−i2i2i2−i2−i2i2i2002-200000000-22i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ3222-2-22-2-22002-202-20-2-22200−i2−i2i2i2−i2−i2i2i200-22000000002-2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ332-22-222-2-22-2-2-2222-22i−2i2i−2i-2200000000000000002i−2i000000002i−2i2i−2i2-22-2000000000000
χ342-22-222-2-22-2-2-2222-22i−2i2i−2i-2200000000000000002i−2i00000000−2i2i−2i2i-22-22000000000000
χ352-22-222-2-22-2-2-2222-2−2i2i−2i2i-220000000000000000−2i2i000000002i−2i2i−2i-22-22000000000000
χ362-22-222-2-22-2-2-2222-2−2i2i−2i2i-220000000000000000−2i2i00000000−2i2i−2i2i2-22-2000000000000
χ372-22-222-2-2-2222-2-2-220000-222-22-22-22-200000000000000000000000000002i−2i2i−2i000000
χ382-22-222-2-2-2222-2-2-220000-222-22-22-22-20000000000000000000000000000−2i2i−2i2i000000
χ392-22-222-2-2-2222-2-2-220000-22-22-22-22-2200000000000000000000000000002i−2i−2i2i000000
χ402-22-222-2-2-2222-2-2-220000-22-22-22-22-220000000000000000000000000000−2i2i2i−2i000000
χ412-22-222-2-2-22-2-2-22222i−2i2i−2i2-22-22-2-22-2200000000−2i2i00002i−2i2i−2i00000000000000000000
χ422-22-222-2-2-22-2-2-22222i−2i2i−2i2-2-22-222-22-200000000−2i2i0000−2i2i−2i2i00000000000000000000
χ432-22-222-2-2-22-2-2-2222−2i2i−2i2i2-22-22-2-22-22000000002i−2i0000−2i2i−2i2i00000000000000000000
χ442-22-222-2-2-22-2-2-2222−2i2i−2i2i2-2-22-222-22-2000000002i−2i00002i−2i2i−2i00000000000000000000
χ452-2-222-22-200-2202-202i−2i−2i2i00i2−i2−i2i2−i2i2i2−i22i−2i000000002-200−222−22−2−22−i2i2i2−i2000000000000
χ462-2-222-22-200-2202-202i−2i−2i2i00i2−i2−i2i2−i2i2i2−i2−2i2i00000000-2200−222−2−222−2i2−i2−i2i2000000000000
χ472-2-222-22-200-2202-202i−2i−2i2i00−i2i2i2−i2i2−i2−i2i22i−2i000000002-2002−2−22−222−2i2−i2−i2i2000000000000
χ482-2-222-22-200-2202-202i−2i−2i2i00−i2i2i2−i2i2−i2−i2i2−2i2i00000000-22002−2−222−2−22−i2i2i2−i2000000000000
χ492-2-222-22-200-2202-20−2i2i2i−2i00i2−i2−i2i2−i2i2i2−i22i−2i00000000-22002−2−222−2−22i2−i2−i2i2000000000000
χ502-2-222-22-200-2202-20−2i2i2i−2i00i2−i2−i2i2−i2i2i2−i2−2i2i000000002-2002−2−22−222−2−i2i2i2−i2000000000000
χ512-2-222-22-200-2202-20−2i2i2i−2i00−i2i2i2−i2i2−i2−i2i22i−2i00000000-2200−222−2−222−2−i2i2i2−i2000000000000
χ522-2-222-22-200-2202-20−2i2i2i−2i00−i2i2i2−i2i2−i2−i2i2−2i2i000000002-200−222−22−2−22i2−i2−i2i2000000000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ54444-4-4-44-44400-400-400000000000000000000000000000000000000000000000022−2200
χ55444-4-4-44-44400-400-4000000000000000000000000000000000000000000000000−222200
χ56444-4-4-44-4-4-4004004000000000000000000004i−4i000000000000000000000000000000
χ57444-4-4-44-4-4-400400400000000000000000000−4i4i000000000000000000000000000000
χ5844-4-44-4-4400-440-4400000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ5944-4-44-4-4400-440-440000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ604-444-4-4-444-400-40040000000000000000004i−4i00000000000000000000000000000000
χ614-444-4-4-444-400-4004000000000000000000−4i4i00000000000000000000000000000000
χ624-444-4-4-44-4400400-400000000000000000000000000000000000000000000002i2−2i20000
χ634-444-4-4-44-4400400-40000000000000000000000000000000000000000000000−2i22i20000
χ644-44-444-4-44-4444-4-4-400004-40000000000000000000000000000000000000000000000
χ654-4-444-44-4004-40-4400000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ664-4-444-44-4004-40-440000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ6788-88-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8-8888000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).